We have created a new runtime type and added some new facets and we would like to make these facets "fixed". However, I can't figure out what configuration we need to set up in the plugin.xml. Any help would be much appreciated.

Controlling the set of fixed facets is the domain of the project wizard. For instance, dynamic web project specifies "java" + "web". A third party that contributes a new facet and wishes to re-use an existing wizard cannot make that facet fixed. Doing so would alter the fundamental characteristics of that wizard.